Solvents, mixed aqueous solubility parameter

Using classical thermodynamics, another relation between the osmotic second virial coefficient and the aqueous solubility was established [35]. In that paper, the aqueous mixed solvent is treated as a single component and the obtained relation contains two adjustable parameters. This equation was used to correlate the osmotic second virial coefficient and the aqueous protein solubility in the systems water-lysozyme-salt (NaCl) and water-ovalbumin-salt ((NH4)2S04). 

As noted in the Introduction, the Cohn equation, (Eq. (1)), considers that log of protein solubility is a linear function of the cosolvent molarity. In reality [5,14], the above dependence is not linear. Fig. 1 presents some accurate experimental data regarding the aqueous solubility of lysozyme and shows that linearity occurs only in the dilute region (C3<0.5). Our Eq. (12) allows one to explain this behavior. Only the dilute region (c3<0.5) is considered because in this composition range the preferential binding parameter is proportional to the concentration of the cosolvent [58,64,69] and Eq. (12) involves this approximation. Eq. (12) reveals that the linearity or nonlinearity of In y2 versus cosolvent concentration depends on the water activity in the protein-free aqueous mixed solvent. Eq. (12) was used to examine the log protein solubility versus eosolvent molarity in water/protein/ polyethylene glycol (PEG) mixtures [42]. It was shown that there were almost linear behaviors for PEG 1000 and PEG... 

Although water is used preferentially as a medium for electrode reactions, there is growing interest in the use of nonaqueous solvents. This is for several reasons first, there are compounds which exhibit very limited solubility in water. Second, some species may not be stable in aqueous media. Third, the range of available potentials, relatively narrow in water, may be wider on both the cathodic and the anodic side in an aptly chosen solvent. Also, some processes of industrial or technical importance are sometimes carried out in nonaqueous or mixed solvents. For instance, in recent years different types of batteries, especially those with lithium electrodes, have been developed and further improved. They are based on the application of nonaqueous solvents. These applications frequently result from the fact that thermodynamic and kinetic parameters of various electrode reactions are greatly affected by the reaction medium. 

Eq. (2) does not contain any adjustable parameter and can be used to predict the gas solubility in mixed solvents in terms of the solubilities in the individual solvents (1 and 3) and their molar volumes. Eq. (2) provided a very good agreement [9] with the experimental gas solubilities in binary aqueous solutions of nonelectrolytes a somewhat modified form correlated well the gas solubilities in aqueous salt solutions [17]. The authors also derived the following rigorous expression for the Henry constant in a binary solvent mixture [9] (Appendix A for the details of the derivation) ... 

The application of UNIFAC to the solid-liquid equilibrium of sohds, such as naphthalene and anthracene, in nonaqueous mixed solvents provided quite accurate results [11]. Unfortunately, the accuracy of UNIFAC regarding the solubility of solids in aqueous solutions is low [7-9]. Large deviations from the experimental activity coefficients at infinite dilution and the experimental octanol/water partition coefficients have been reported [8,9] when the classical old version of UNIFAC interaction parameters [4] was used. To improve the prediction of the activity coefficients at infinite dilution and of the octanol/water partition coefficients of environmentally significant substances, special ad hoc sets of parameters were introduced [7-9]. The reason is that the UNIFAC parameters were determined mostly using the equihbrium properties of mixtures composed of low molecular weight molecules. Also, the UNIFAC method cannot be applied to the phase equilibrium in systems containing... 

The present paper deals with the application of the fluctuation theory of solutions to the solubility of poorly soluble drugs in aqueous mixed solvents. The fluctuation theory of ternary solutions is first used to derive an expression for the activity coefficient of a solute at infinite dilution in an ideal mixed solvent and, further, to obtain an equation for the solubility of a poorly soluble solid in an ideal mixed solvent. Finally, this equation is adapted to the solubility of poorly soluble drugs in aqueous mixed solvents by treating the molar volume of the mixed solvent as nonideal and including one adjustable parameter in its expression. The obtained expression was applied to 32 experimental data sets and the results were compared with the three parameter equations available in the literature. 

In a previous paper (Ruckenstein and Shulgin, 2003), the Kirkwood-Buff theory of solutions (Kirkwood and Buff, 1951) was employed to obtain an expression for the solubility of a solid (particularly a drug) in binary mixed (mainly aqueous) solvents. A rigorous expression for the composition derivative of the activity coefficient of a solute in a ternary solution (Ruckenstein and Shulgin, 2001) was used to derive an equation for the activity coefficient of the solute at infinite dilution in an ideal binary mixed solvent and further for the solubility of a poorly soluble solid. By considering that the excess volume of the mixed solvent depends on composition, the above equation was modified empirically by including one adjustable parameter. The modified equation was compared with the other three-parameter equations available in the literature to conclude that it provided a better agreement. 

The Flory-Huggins interaction parameter (x) and the Wilson parameters (L13 and L31) are considered here adjustable parameters and are calculated from the experimental data regarding the solubility of drugs in aqueous mixed solvents. 

One can see from Tables 1 and 2 that our methods for the correlation of the solubility of drugs in aqueous mixed solvents provide accurate and reliable results. A comparison with the models available in the literature (Table 2) demonstrates that our Eq. (6) provides slightly better results than the best literature models with the same number of parameters. 

The application of UNIFAC to the solubility of naphthalene in nonaqueous mixed solvents provided satisfactory results when compared to experimental data (Acree, 1984). However, the UNIFAC was inaccurate in predicting the solubilities of solids in aqueous solutions (Fan and Jafvert, 1997). Furthermore, the application of the traditional UNIFAC to mixtures containing a polymer or another large molecule, such as a drug, and low molecular weight solvents is debatable (Fredenslund and Sprensen, 1994). The reason is that the UNIFAC parameters were determined mostly... 

Eq. (28) thus obtained can be used to represent the solubility of poorly soluble drugs in aqueous mixed solvents if information about the properties of the binary solvent (composition, phase equilibria and molar volume), the nonideality parameters and the constant A is available. These parameters can be considered as adjustable, and determined by fitting the experimental solubilities in the binary solvent. We applied such a procedure to the solubilities of caffeine in water/AW-dimethylformamide (Herrador and Gonzalez, 1997) and water/1,4-dioxane (Adjei et al., 1980), of sulfamethizole in water/1,4-dioxane (Reillo et al., 1995) as well as of five solutes in water/ propylene glycol (Rubino and Obeng, 1991). It was shown that Eq. (28) provides accurate correlations of the experimental data. 

The present paper is devoted to the derivation of a relation between the preferential solvation of a protein in a binary aqueous solution and its solubility. The preferential binding parameter, which is a measure of the preferential solvation (or preferential hydration) is expressed in terms of the derivative of the protein activity coefficient with respect to the water mole fraction, the partial molar volume of protein at infinite dilution and some characteristics of the protein-free mixed solvent. This expression is used as the starting point in the derivation of a relationship between the preferential binding parameter and the solubility of a protein in a binary aqueous solution. 

Keywords Protein Aqueous mixed solvent Preferential binding parameter Solubility... 

The aim of the present paper is to establish a relation between (1) the preferential solvation (or hydration) of a protein and (2) the protein solubility in an aqueous mixed solvent. The obtained relation will be used to predict the protein solubility in an aqueous solvent in terms of the preferential binding parameter. 

A relationship between the derivative of the activity coefficient of the protein with respect to the mole fraction of water at infinite dilution of protein and the preferential binding parameter was used to connect the solubility of a protein in an aqueous mixed solvent to the preferential binding parameter. This relation was used to examine the salting-in and salting-out effect of various compounds on the protein solubility in water and to predict the protein solubility. 

In this paper, the Kirkwood-Buff theory of solutions is used to examine the effect of PEG on aqueous protein solutions, the focus being on the local composition of the mixed solvent in the vicinity of the protein molecule and on the protein solubility. The theoretical considerations led to equations that coimect the experimental preferential binding parameter with the excess (or deficit) numbers of water and cosolvent molecules around a protein molecule. Calculations were carried out for various proteins in various PEG solutions. The results showed that in all cases the proteins were preferentially hydrated. Evidence was also brought that the hydration is a result of steric exclusion. 

Timasheff and coworkers [5,59-63] were the first to notice that there is a connection between the preferential binding parameter and the aqueous protein solubility. On the basis of their measurements and literature data regarding the preferential binding parameter and the aqueous protein solubility, they concluded that there is a general correlation between these quantities [5,59-63]. Particularly, they concluded that preferential hydration of a protein (/I < 0) is equivalent to a salting-out behavior, i.e. the addition of a cosolvent decreases the protein solubility [5,65]. Thus, the local composition of the components of a mixed solvent is one of the most important factors affecting the aqueous protein solubility [5,40,59-63]. 

The authors of the present paper have developed a theory which connects the preferential binding parameter and the aqueous protein solubility [41,42]. The central element of the theory is the following relation (its derivation is provided in the Appendix) which relates the solubility of a protein to the mixed solvent composition and the preferential binding parameter [41,42] ... 

Therefore, important parameters such as phase transfer phenomena (i.e. solubility of the reactants in the ionic liquid phase), volume ratio of the different phases, efficiency of mixing so as to provide maximum liquid-liquid interfacial area, are key factors in determining and controlling reaction rates and kinetics. Kinetic models have been developed for aqueous biphasic systems and are continuously refined to improve agreement with experimental results. These models might be transferable to biphasic catalysis with ionic liquids, but more data concerning the solubility ofliq-uids (and gas) in these new solvents and the existence of phase equilibria in the presence of organic upper phases have still to be accumulated (see Sections 3.3 and 3.4). 

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